Structure constants of planar N =4 Yang Mills at one loop

We study structure constants of gauge invariant operators in planar N=4 Yang-Mills at one loop with the motivation of determining features of the string dual of weak coupling Yang-Mills. We derive a simple renormalization group invariant formula characterizing the corrections to structure constants of any primary operator in the planar limit. Applying this to the scalar SO(6) sector we find that the one loop corrections to structure constants of gauge invariant operators is determined by the one loop anomalous dimension Hamiltonian in this sector. We then evaluate the one loop corrections to structure constants for scalars with arbitrary number of derivatives in a given holomorphic direction. We find that the corrections can be characterized by suitable derivatives on the four point tree function of a massless scalar with quartic coupling. We show that individual diagrams violating conformal invariance can be combined together to restore it using a linear inhomogeneous partial differential equation satisfied by this function.Comment: 52 pages, 12 figures, Typos fixed, reference adde

Towards a string bit formulation of N=4 super Yang-Mills

We show that planar cal N=4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence between the on shell gauge invariant words of the free Y-M theory and the states in the oscillators' Hilbert space, obeying a local gauge and cyclicity constraints. The planar two-point functions and the three-point functions of all gauge invariant words are obtained by the simple delta-function overlap of the corresponding discrete string world sheet. At first order in the 't Hooft coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of the planar two-point and the three-point functions can be incorporated by nearest neighbour interactions among the discretized string bits. In the SU(2) sub-sector we show that the one-loop corrections to the structure constants can be uniquely determined by the symmetries of the bit picture. For the SU(2) sub-sector we construct a gauged, linear, discrete world-sheet model for the oscillators, with only nearest neighbour couplings, which reproduces the anomalous dimension Hamiltonian up to two loops. This model also obeys BMN scaling to all loops.Comment: 64 pages, 6 figures, typos fixed, references adde

Understanding possible electromagnetic counterparts to loud gravitational wave events: Binary black hole effects on electromagnetic fields

In addition to producing loud gravitational waves (GW), the dynamics of a binary black hole system could induce emission of electromagnetic (EM) radiation by affecting the behavior of plasmas and electromagnetic fields in their vicinity. We here study how the electromagnetic fields are affected by a pair of orbiting black holes through the merger. In particular, we show how the binary's dynamics induce a variability in possible electromagnetically induced emissions as well as an enhancement of electromagnetic fields during the late-merge and merger epochs. These time dependent features will likely leave their imprint in processes generating detectable emissions and can be exploited in the detection of electromagnetic counterparts of gravitational waves.Comment: 12 page

Black Holes at the IceCube Neutrino Telescope

If the fundamental Planck scale is about a TeV and the cosmic neutrino flux is at the Waxman-Bahcall level, quantum black holes are created daily in the Antarctic ice-cap. We re-examine the prospects for observing such black holes with the IceCube neutrino-detection experiment. To this end, we first revise the black hole production rate by incorporating the effects of inelasticty, i.e., the energy radiated in gravitational waves by the multipole moments of the incoming shock waves. After that we study in detail the process of Hawking evaporation accounting for the black hole's large momentum in the lab system. We derive the energy spectrum of the Planckian cloud which is swept forward with a large, O (10^6), Lorentz factor. (It is noteworthy that the boosted thermal spectrum is also relevant for the study of near-extremal supersymmetric black holes, which could be copiously produced at the LHC.) In the semiclassical regime, we estimate the average energy of the boosted particles to be less than 20% the energy of the neutrino-progenitor. Armed with such a constraint, we determine the discovery reach of IceCube by tagging on "soft" (relative to what one would expect from charged current standard model processes) muons escaping the electromagnetic shower bubble produced by the black hole's light descendants. The statistically significant 5-sigma excess extends up to a quantum gravity scale ~ 1.3 TeV.Comment: Matching version to be published in Phys. Rev.

Reinforcement Learning Dynamics in Social Dilemmas

In this paper we replicate and advance Macy and Flache\'s (2002; Proc. Natl. Acad. Sci. USA, 99, 7229–7236) work on the dynamics of reinforcement learning in 2�2 (2-player 2-strategy) social dilemmas. In particular, we provide further insight into the solution concepts that they describe, illustrate some recent analytical results on the dynamics of their model, and discuss the robustness of such results to occasional mistakes made by players in choosing their actions (i.e. trembling hands). It is shown here that the dynamics of their model are strongly dependent on the speed at which players learn. With high learning rates the system quickly reaches its asymptotic behaviour; on the other hand, when learning rates are low, two distinctively different transient regimes can be clearly observed. It is shown that the inclusion of small quantities of randomness in players\' decisions can change the dynamics of the model dramatically.Reinforcement Learning; Replication; Game Theory; Social Dilemmas; Agent-Based; Slow Learning

Quantum interference oscillations of the superparamagnetic blocking in an Fe8 molecular nanomagnet

We show that the dynamic magnetic susceptibility and the superparamagnetic blocking temperature of an Fe8 single molecule magnet oscillate as a function of the magnetic field Hx applied along its hard magnetic axis. These oscillations are associated with quantum interferences, tuned by Hx, between different spin tunneling paths linking two excited magnetic states. The oscillation period is determined by the quantum mixing between the ground S=10 and excited multiplets. These experiments enable us to quantify such mixing. We find that the weight of excited multiplets in the magnetic ground state of Fe8 amounts to approximately 11.6%.Comment: Accepted in Phys. Rev. Let

Fortran and C programs for the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap

Many of the static and dynamic properties of an atomic Bose-Einstein condensate (BEC) are usually studied by solving the mean-field Gross-Pitaevskii (GP) equation, which is a nonlinear partial differential equation for short-range atomic interaction. More recently, BEC of atoms with long-range dipolar atomic interaction are used in theoretical and experimental studies. For dipolar atomic interaction, the GP equation is a partial integro-differential equation, requiring complex algorithm for its numerical solution. Here we present numerical algorithms for both stationary and non-stationary solutions of the full three-dimensional (3D) GP equation for a dipolar BEC, including the contact interaction. We also consider the simplified one- (1D) and two-dimensional (2D) GP equations satisfied by cigar- and disk-shaped dipolar BECs. We employ the split-step Crank-Nicolson method with real- and imaginary-time propagations, respectively, for the numerical solution of the GP equation for dynamic and static properties of a dipolar BEC. The atoms are considered to be polarized along the z axis and we consider ten different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar BEC in 1D (along x and z axes), 2D (in x-y and x-z planes), and 3D, and we provide working codes in Fortran 90/95 and C for these ten cases (twenty programs in all). We present numerical results for energy, chemical potential, root-mean-square sizes and density of the dipolar BECs and, where available, compare them with results of other authors and of variational and Thomas-Fermi approximations.Comment: To download the programs click other and download sourc